Question

a decorative block is shown which is made of two solids a cube and a hemisphere the base of the block is a cube with edge 6cm and the hemisphere fixed on the top has a diameter of 4.2cm find the total surface area of the block and the volume of the block formed

Answer 1

Part a: The total surface area of the block is $229.85 \ {cm}^{2}$

Part b: The volume of the block is

Explanation:

Part a: The total surface area of the cube is given by

$TSA= 6a^2$

        $=6(6)^2$

        $=216 \ cm^2$

Thus, the total surface area of the cube is $216 \ {cm}^{2}$

The diameter of the hemisphere is $4.2 \ cm$

$Radius = \frac{d}{2} =\frac{4.2}{2} =2.1$

The surface area of the block = TSA of cube + CSA of hemisphere - base area of hemisphere

Surface area of the block = $216+2\pi r^2- \pi r^2$

                                          $=216+\pi r^2$

                                          $=216+(3.14)(2.1)^2$

                                          $=216+13.85$

                                          $=229.85 \ cm^2$

Thus, the surface area of the block is $229.85 \ {cm}^{2}$

Part b: The volume of the cube is given by

$V=a^3$

   $=6^3$

   $=216$

Thus, the volume of the cube is $216\ cm^3$

The volume of the hemisphere is given by

$V=\frac{2}{3} \pi r^3$

   $=\frac{2}{3} (3.14)(2.1)^3$

   $=\frac{2}{3} (3.14)(9.261)$

   $=19.39 \ cm^3$

Thus, the volume of the hemisphere is $19.39 \ cm^3$

The volume of the block = volume of the cube + volume of the hemisphere

Volume of the block $=216+19.39$

                                  $=235.39 \ cm^3$

Thus, the volume of the block is $235.39 \ {cm}^{3}$

Learn more:

(1) A decorative block is shown which is made up of two solids a cube and hemisphere the base of the block is a cube with edge 6 cm and hemisphere fixed on the top has diameter 4.2 cm find total surface area of the block

brainly.in/question/8625284

(2) A decorative block which is made of two solids , a cube and a hemisphere. The base of the block is a cube with edge 5 cm , and the hemisphere fixed on the top has a diameter 4.2 cm.Find the total surface area of the block .

(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

brainly.in/question/2088847

Answer 2

Given :-

• A decorative block is shown which is made of two solids a cube and a hemisphere the base of the block is a cube with edge 6cm and the hemisphere fixed on the top has a diameter of 4.2cm

To find :-

• Total surface area of the block and the volume of the block formed

Solution :-

It is given that decorative block which is made of two solids a cube and a hemisphere

• Edge of a cube = 6cm

• Diameter of hemisphere = 4.2cm

• Radius of hemisphere = 4.2/2cm

Firstly we have to find total surface area of cube

→ 6a² (a is the side of a cube)

→ 6 × 6 × 6

→ 216 cm²

So, total surface area of cube is 216cm²

Now, surface area of decorative block

• Note : Don't include that part of cube where the hemisphere is attached

→ Total surface area of cube - base area of hemisphere + curved surface area of hemisphere

→ 216 - πr² + 2πr²

→ 216 + πr²

→ 216 + 22/7 × 4.2/2 × 4.2/2

→ 216 + 22/7 × 2.1 × 2.1

→ 216 + 22 × 0.3 × 2.1

→ 216 + 6.6 × 2.1

→ 216 + 13.86

→ 229.86cm²

Now, volume of decorative block

→ Volume of cube + volume of hemisphere

→ a³ + 2/3 πr³

Put the value of cube edge and radius of hemisphere

→ (6)³ + 2/3 × 22/7 × 4.2/2 × 4.2/2 × 4.2/2

→ 216 + 2/3 × 22/7 × 2.1 × 2.1 × 2.1

→ 216 + 2 × 22 × 0.3 × 0.7 × 2.1

→ 216 + 44 × 0.21 × 2.1

→ 216 + 19.404

→ 235.404 cm³

Hence,

• Volume of decorative block is 235.404cm³

• Total surface area of decorative block is 229.86cm²